A large truck bomb has rocked the centre of Cairo, killing at least four people and injuring 76.

The explosion early on Friday morning – the eve of the third anniversary of the 2011 uprising that toppled President Hosni Mubarak – struck the Egyptian police headquarters.

Hours after the attack, two more blasts hit the capital.

A crude explosive device killed one policeman and wounded nine others in another Cairo neighbourhood, the interior ministry said in a statement. Security sources said a person driving past security vehicles threw a hand grenade in their direction.

In Giza, a large district on the outskirts of Cairo, a third explosion went off near a police station. There were no immediate reports of casualties.

The first blast occurred shortly after 6.30am, about half an hour after the closure of a nearby security checkpoint, according to Mahmoud Abdel Sattar, a 27-year-old sergeant on duty on the third floor of the building."A big truck exploded outside the fence – it didn't get inside the [forecourt of the] security headquarters itself," Sattar said. "After the explosion, a white private car with four passengers started shooting on the buildings as well."Sattar was hit by falling masonry. "There was gunfire between the two sides. Everyone started running and there were a lot of injuries."The blast caused a large crater outside the building that quickly filled with water. An official at the scene said it was 4 metres deep.The immediate aftermath was chaotic, said Abdelrahman Mohsen, a 27-year-old furniture maker who arrived on the scene shortly after the explosion, and helped to carry away the casualties."I saw at least four bodies on the floor, and then we carried four more," said Mohsen, who could not confirm if the victims were dead. "There were a lot of police conscripts going inside and trying to find their friends, and there was masonry falling down on them in front of the building."

A man carries an Egyptian police officer to an ambulance after the bombing. Photograph: Khalil Hamra/AP

The explosion, heard from several miles away, smashed windows, collapsed house walls and warped the shutters of shopfronts.Onlookers immediately blamed Muslim Brotherhood, the Islamist group of the deposed president Mohamed Morsi, which has been scapegoated for a rise in terrorist attacks since his ousting. Officials have provided no evidence of their involvement.

"The people demand the execution of the Brotherhood," chanted a crowd of bystanders, some of whom carried pictures of General Abdel Fattah al-Sisi, the army chief who ousted Morsi.Two mobs attacked a van and a bystander suspected by some of being members of the Brotherhood. Further down the road, police officers advised drivers with beards – a sign of religious piety – to turn around to avoid being attacked.A Muslim Brotherhood-led coalition has planned nationwide protests after Friday prayers as part of their near-daily demonstrations against the overthrow of Morsi and the recent vote on the country's rewritten constitution.

Twenty nine have been killed, the majority of them in Cairo, where police tried to stop people entering Tahrir Square during marches on the third anniversary of the uprising that culminated in the overthrow of president Hosni Mubarak